A141402 - OEIS

%I #7 Mar 31 2021 01:28:02

%S 0,1,1,4,8,4,9,25,25,9,16,52,80,52,16,25,89,169,169,89,25,36,136,292,

%T 360,292,136,36,49,193,449,625,625,449,193,49,64,260,640,964,1088,964,

%U 640,260,64,81,337,865,1377,1681,1681,1377,865,337,81,100,424,1124,1864,2404,2600,2404,1864,1124,424,100

%N Triangle T(n, k) = n^2 + (2*k*(n-k))^2, read by rows.

%H G. C. Greubel, <a href="/A141402/b141402.txt">Rows n = 0..50 of the triangle, flattened</a>

%F T(n, k) = n^2 + (2*k*(n-k))^2.

%F Sum_{k=0..n} T(n, k) = n*(2*n^4 + 15*n^2 + 15*n -2)/15. - _G. C. Greubel_, Mar 30 2021

%e Triangle begins as:

%e     0;

%e     1,   1;

%e     4,   8,    4;

%e     9,  25,   25,    9;

%e    16,  52,   80,   52,   16;

%e    25,  89,  169,  169,   89,   25;

%e    36, 136,  292,  360,  292,  136,   36;

%e    49, 193,  449,  625,  625,  449,  193,   49;

%e    64, 260,  640,  964, 1088,  964,  640,  260,   64;

%e    81, 337,  865, 1377, 1681, 1681, 1377,  865,  337,  81;

%e   100, 424, 1124, 1864, 2404, 2600, 2404, 1864, 1124, 424, 100;

%p A141402:= (n,k)-> n^2 + (2*k*(n-k))^2;

%p seq(seq(A141402(n,k), k=0..n), n=0..12); # _G. C. Greubel_, Mar 30 2021

%t T[n_, k_]:= n^2 + (2*k*(n-k))^2;

%t Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten

%o (Magma) [n^2 + (2*k*(n-k))^2: k in [0..n], n in [0..12]]; // _G. C. Greubel_, Mar 30 2021

%o (Sage) flatten([[n^2 + (2*k*(n-k))^2 for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 30 2021

%K nonn,easy,tabl

%O 0,4

%A _Roger L. Bagula_, Aug 03 2008

%E Edited by _G. C. Greubel_, Mar 30 2021